SOLUTION: solve the equation 256^x= 64^x+4

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: solve the equation 256^x= 64^x+4      Log On


   

Question 243551: solve the equation
256^x= 64^x+4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
256%5E%28x%29=+64%5E%28x%2B4%29 Start with the given equation.


%282%5E8%29%5E%28x%29=+%282%5E6%29%5E%28x%2B4%29 Rewrite 256 as 2%5E8 and 64 as 2%5E6


2%5E%288x%29=+2%5E%286%28x%2B4%29%29 Multiply the exponents.


8x=6%28x%2B4%29 Since the bases are equal, the exponents are equal.


8x=6x%2B24 Distribute.


8x-6x=24 Subtract 6x from both sides.


2x=24 Combine like terms on the left side.


x=%2824%29%2F%282%29 Divide both sides by 2 to isolate x.


x=12 Reduce.


----------------------------------------------------------------------

Answer:

So the solution is x=12